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Inverse Laplace transform

  1. Oct 16, 2006 #1
    Hi I'm having problems find the inverse Laplace transform of [tex]\frac{s}{{\left( {s + 4} \right)^4 }}[/tex] via a table/look up method.

    In another question part I found the inverse Laplace transform of (s+4)^-4 by considering [tex]\frac{{d^3 }}{{db^3 }}\left[ {\left( {s + b} \right)^{ - 1} } \right][/tex] so that the problem essentially reduced to finding the inverse Laplace transform of 1/(s+b). After that I just set b = 4 to get the answer.

    But I can't think of a way to do this one (the one in the first sentence of this post). I have [tex]L^{ - 1} \left\{ {\frac{1}{{\left( {s + 4} \right)^4 }};s \to t} \right\} = \frac{{t^3 }}{6}e^{ - 2t} [/tex] but I don't see a way to use it to find the inverse Laplace transform of s(s+4)^-4. Can someone please help me out? Thanks.
  2. jcsd
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